Question

A sum of x rupees was divided between A, B, C, and D in the ratio 1/3:1/7:1/2:1 .Difference between the shares of D and B is 47 rupees more than the sum of shares of A and C then , find the total sum of money.​

Answer 1

ANSWER:

Given:

• Sum of x rupees is divided into A, B, C and D.
• Ratio of shares of A, B, C and D = 1/3 : 1/7 : 1/2 : 1
• Difference between shares of D and B = Rs 47 + Sum of shares of A and C

To Find:

• Total Sum of money

Solution:

We are given that, total money is x.

Also, we are given that,

⇒ Ratio of shares of A, B, C and D = 1/3 : 1/7 : 1/2 : 1

So, let shares of A, B, C and D be 1y/3, 1y/7, 1y/2 and y.

So,

⇒ y/3 + y/7 + y/2 + y = x

Taking LCM,

⇒ (14y + 6y + 21y + 42y)/42 = x

⇒ 83y = 42x

So,

⇒ x = 83y/42 -----(1)

Also,

⇒ y - y/7 = 47 + y/3 + y/2

Taking LCM,

⇒ (7y - y)/7 = (282 + 2y + 3y)/6

⇒ 6y/7 = (5y + 282)/6

On cross multiplying,

⇒ 36y = 35y + 1974

So,

⇒ 36y - 35y = 1974

Hence,

⇒ y = 1974

Substituting value of y in (1),

⇒ x = 83y/42

⇒ x = 83(1974)/42

⇒ x = 83 × 47

⇒ x = 3901

Hence, the total amount is Rs 3901.